First, preheat your oven to 325F. Cut your pork shoulder into about 4 very large chunks. Pat dry, then season generously with kosher salt & black pepper on all sides. Bring your dutch oven up to medium-high heat. Once hot, add a light amount of oil. Then, add pork shoulder (you will likely have to cook it in 2 batches to avoid overcrowding the pot), and sear for about 2-3 minutes on each side, or until golden. Remove pork from the pot and set aside.
3.5 lbs boneless pork shoulder, kosher salt & black pepper, olive oil
Reduce heat to medium. At this point, there should be plenty of fat in the pot, but if not, add a bit more olive oil. Then, add onion, season with kosher salt & saute for 3-4 minutes. Add in garlic and cook for 1 more minute.
1 medium yellow onion, 5 garlic cloves
Deglaze the pan with apple cider, scraping up any browned bits at the bottom of the pot. Add in the broth and apple cider vinegar and stir. Then, add back in the pork shoulder along with the sliced apples and the herbs. The liquid should go about ½-¾ of the way up the pork, if not add a bit more broth.
1 granny smith apple, 2 cups apple cider, 1 cup chicken broth, 2 tsp apple cider vinegar, 4 sprigs fresh thyme, 4 sage leaves
Increase the heat and bring it up to a boil. Then, cover the pot with a lid and transfer to the oven to braise for about 3-3.5 hours, or until the pork is super tender. Remove pork from the pot and shred with two forks.
Strain all of the solids out, place the pot of liquid back onto the stovetop and bring up to medium-low heat. Allow it to simmer and reduce by half, about 10-15 minutes. You can use this to drizzle over the finished tacos.